Is it permitted to trim a mustache during sefira if it is not bothering the person in any way with regards to eating but is bothering him in other ways?
See this article which seems to be a comprehensive summary (I know that's an oxymoron, but you can read the article, anyway ;-). In it, you'll find many cross-refs.
The only permissions to shave are if it interferes with eating, as you mentioned, health reasons, and certain simchot where you are a "direct participant" e.g. your son is having a brit, you're a chatan, etc. You can't trim your mustache if your shidduch "date" will find your mustache ugly. (IMO, if that's a criterion for the date to break a shidduch, consider yourself lucky.) There is no mention regarding other "bothersome" permissibility.